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Optics Express

Generating path entangled states in waveguide systems with second-order nonlinearity

Alexandre Belsley, Thomas Pertsch, Frank Setzpfandt

Published Aug 7, 2020• 14 citations
Publisher

Abstract

Spontaneous parametric down-conversion in coupled nonlinear waveguides is a flexible approach for generating tunable path entangled states. We describe a formalism based on the Cayley-Hamilton theorem to compute the quantum states generated by waveguide arrays for arbitrary system parameters. We find that all four Bell states can be generated in directional couplers with non-degenerate photons. Our method enables one to efficiently explore the phase space of waveguide systems and readily assess the robustness of any given state to variations in the system's parameters. We believe it represents a valuable tool for quantum state engineering in coupled waveguide systems.

DOI
10.1364/oe.401303

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Spontaneous parametric down-conversion in coupled nonlinear waveguides is a flexible approach for generating tunable path entangled states. We describe a formalism based on the Cayley-Hamilton theorem to compute the quantum states generated by waveguide arrays for arbitrary system parameters. We find that all four Bell states can be generated in directional couplers with non-degenerate photons. Our method enables one to efficiently explore the phase space of waveguide systems and readily assess the robustness of any given state to variations in the system's parameters. We believe it represents a valuable tool for quantum state engineering in coupled waveguide systems.
Abstract The on‐chip integration of quantum light sources has enabled the realization of complex quantum photonic circuits. However, for the practical implementation of such circuits in quantum information applications, it is crucial to develop sources delivering entangled quantum photon states with on‐demand tunability. Here we propose and experimentally demonstrate the concept of a widely tunable quantum light source based on spontaneous parametric down‐conversion in a simple nonlinear directional coupler. We show that spatial photon‐pair correlations and entanglement can be reconfigured on‐demand by tuning the phase difference between the pump beams and the phase mismatch inside the structure. We experimentally demonstrate the generation of split states, robust N00N states, various intermediate regimes and biphoton steering on a single chip. Furthermore we theoretically investigate other regimes allowing all‐optically tunable generation of all Bell states and flexible control of path‐energy entanglement. Such wide‐range capabilities of a structure comprised of just two coupled nonlinear waveguides are attributed to the intricate interplay between linear coupling and nonlinear phase matching. This scheme provides an important advance towards the realization of reconfigurable quantum circuitry. image
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA. The on-chip integration of quantum light sources has enabled the realization of complex quantum photonic circuits. However, for the practical implementation of such circuits in quantum information applications, it is crucial to develop sources delivering entangled quantum photon states with on-demand tunability. Here we propose and experimentally demonstrate the concept of a widely tunable quantum light source based on spontaneous parametric down-conversion in a simple nonlinear directional coupler. We show that spatial photon-pair correlations and entanglement can be reconfigured on-demand by tuning the phase difference between the pump beams and the phase mismatch inside the structure. We experimentally demonstrate the generation of split states, robust N00N states, various intermediate regimes and biphoton steering on a single chip. Furthermore we theoretically investigate other regimes allowing all-optically tunable generation of all Bell states and flexible control of path-energy entanglement. Such wide-range capabilities of a structure comprised of just two coupled nonlinear waveguides are attributed to the intricate interplay between linear coupling and nonlinear phase matching. This scheme provides an important advance towards the realization of reconfigurable quantum circuitry. An integrated all-optically tunable source of two-photon quantum states based on spontaneous parametric down-conversion is experimentally demonstrated in a directional coupler consisting of two lithium niobate waveguides. The degree of entanglement and shape of two-photon spatial correlations is widely tunable by varying the phase mismatch and relative phases of the two pump beams. The operating principle is suitable for practical implementation of reconfigurable photon sources in on-chip quantum circuits.
Integrated optical devices are expected to play a promising role in the field of quantum information science and technology. In this paper we propose a scheme for the generation of nondegenerate, copolarized, modal, and path-entangled photons using a directional coupler and an asymmetric Y\mathsf{Y}Y-coupler geometry in type-0 phase-matched domain-engineered lithium niobate (LN) waveguide. The nonlinearity in LN is tailored in such a way that quasi-phase-matching conditions for two different spontaneous parametric down-conversion processes are obeyed simultaneously, leading to a modal and path-entangled state at the output. Assuming typical values of various parameters, we show, through numerical simulations, that an almost maximally entangled state is achievable over a wide range of waveguide parameters. For the degenerate case, the proposed scheme gives a NOON state for NNN === 2. The generated entangled photon pairs should have potential applications in quantum information schemes and also in quantum metrology. By appropriate domain engineering and component designing, the idea can be further extended to generate hyperentangled and two-photon multipath-entangled states, which may have further applications in quantum computation protocols.
We propose the use of nonlinear periodic waveguides for direct and fully integrated generation of counterpropagating photon pairs by spontaneous parametric down-conversion. Using the unique properties of Bloch modes in such periodic structures, we furthermore show that two counterpropagating phase-matching conditions can be fulfilled simultaneously, allowing for the generation of path-entangled Bell states in a single periodic waveguide. To demonstrate the feasibility of our proposal, we design a photonic crystal slab waveguide made of lithium niobate and numerically demonstrate Bell-state generation.
Encoding continuous-variable quantum information in the optical domain has recently enabled the generation of large entangled states, yet robust implementation remains a challenge. Here, we present a straightforward protocol for generating multipartite entanglement based on spontaneous parametric down-conversion in a circular array of quadratic nonlinear waveguides. We provide a rigorous theoretical framework, including comprehensive derivations of the propagation equations and the identification of regimes where analytical solutions are possible. Crucially, our approach identifies the pump and detection configurations required to sustain and measure multipartite full inseparability across arbitrary propagation distances and for any number of waveguides N=4nN=4 nN=4n. This regime, elusive to standard numerical methods, represents a key requirement for scalable quantum protocols. Our scheme is inherently robust as it relies on phase-matched propagation eigenmodes, making it resilient against variations in sample length, coupling, and nonlinearity.
Harnessing high-dimensional entangled states of light presents a frontier for advancing quantum information technologies, from fundamental tests of quantum mechanics to enhanced computation and communication protocols. In this context, the spatial degree of freedom stands out as particularly suited for on-chip integration. But while traditional demonstrations produce and manipulate path-entangled states sequentially with discrete optical elements, continuously-coupled nonlinear waveguide systems offer a promising alternative where photons can be generated and interfere along the entire propagation length, unveiling novel capabilities within a reduced footprint. Here we exploit this concept to implement a compact and reconfigurable source of path-entangled photon pairs based on parametric down-conversion in semiconductor AlGaAs nonlinear waveguides arrays.